8 research outputs found
Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
We consider the effect of quenched spatial disorder on systems of
interacting, pinned non-Abelian anyons as might arise in disordered Hall
samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension,
such disordered anyon models have previously been shown to exhibit a hierarchy
of infinite randomness phases. Here, we address systems in two spatial
dimensions and report on the behavior of Ising and Fibonacci anyons under the
numerical strong-disorder renormalization group (SDRG). In order to manage the
topology-dependent interactions generated during the flow, we introduce a
planar approximation to the SDRG treatment. We characterize this planar
approximation by studying the flow of disordered hard-core bosons and the
transverse field Ising model, where it successfully reproduces the known
infinite randomness critical point with exponent \psi ~ 0.43. Our main
conclusion for disordered anyon models in two spatial dimensions is that
systems of Ising anyons as well as systems of Fibonacci anyons do not realize
infinite randomness phases, but flow back to weaker disorder under the
numerical SDRG treatment.Comment: 12 pages, 12 figures, 1 tabl
Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass
We investigate the performance of flat-histogram methods based on a
multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional
+/- J spin glass by measuring round-trip times in the energy range between the
zero-temperature ground state and the state of highest energy. Strong
sample-to-sample variations are found for fixed system size and the
distribution of round-trip times follows a fat-tailed Frechet extremal value
distribution. Rare events in the fat tails of these distributions corresponding
to extremely slowly equilibrating spin glass realizations dominate the
calculations of statistical averages. While the typical round-trip time scales
exponential as expected for this NP-hard problem, we find that the average
round-trip time is no longer well-defined for systems with N >= 8^3 spins. We
relate the round-trip times for multicanonical sampling to intrinsic properties
of the energy landscape and compare with the numerical effort needed by the
genetic Cluster-Exact Approximation to calculate the exact ground state
energies. For systems with N >= 8^3 spins the simulation of these rare events
becomes increasingly hard. For N >= 14^3 there are samples where the
Wang-Landau algorithm fails to find the true ground state within reasonable
simulation times. We expect similar behavior for other algorithms based on
multicanonical sampling.Comment: 9 pages, 12 figure
Feedback-optimized parallel tempering Monte Carlo
We introduce an algorithm to systematically improve the efficiency of
parallel tempering Monte Carlo simulations by optimizing the simulated
temperature set. Our approach is closely related to a recently introduced
adaptive algorithm that optimizes the simulated statistical ensemble in
generalized broad-histogram Monte Carlo simulations. Conventionally, a
temperature set is chosen in such a way that the acceptance rates for replica
swaps between adjacent temperatures are independent of the temperature and
large enough to ensure frequent swaps. In this paper, we show that by choosing
the temperatures with a modified version of the optimized ensemble feedback
method we can minimize the round-trip times between the lowest and highest
temperatures which effectively increases the efficiency of the parallel
tempering algorithm. In particular, the density of temperatures in the
optimized temperature set increases at the "bottlenecks'' of the simulation,
such as phase transitions. In turn, the acceptance rates are now temperature
dependent in the optimized temperature ensemble. We illustrate the
feedback-optimized parallel tempering algorithm by studying the two-dimensional
Ising ferromagnet and the two-dimensional fully-frustrated Ising model, and
briefly discuss possible feedback schemes for systems that require
configurational averages, such as spin glasses.Comment: 12 pages, 14 figure
One-particle density matrix and momentum distribution function of one-dimensional anyon gases
We present a systematic study of the Green functions of a one-dimensional gas
of impenetrable anyons. We show that the one-particle density matrix is the
determinant of a Toeplitz matrix whose large N asymptotic is given by the
Fisher-Hartwig conjecture. We provide a careful numerical analysis of this
determinant for general values of the anyonic parameter, showing in full
details the crossover between bosons and fermions and the reorganization of the
singularities of the momentum distribution function.
We show that the one-particle density matrix satisfies a Painleve VI
differential equation, that is then used to derive the small distance and large
momentum expansions. We find that the first non-vanishing term in this
expansion is always k^{-4}, that is proved to be true for all couplings in the
Lieb-Liniger anyonic gas and that can be traced back to the presence of a delta
function interaction in the Hamiltonian.Comment: 21 pages, 4 figure
Ensemble optimization techniques for the simulation of slowly equilibrating systems
Competing phases or interactions in complex many-particle systems can result in free energy barriers that strongly suppress thermal equilibration. Here we discuss how extended ensemble Monte Carlo simulations can be used to study the equilibrium behavior of such systems. Special focus will be given to a recently developed adaptive Monte Carlo technique that is capable to explore and overcome the entropic barriers which cause the slow-down. We discuss this technique in the context of broad-histogram Monte Carlo algorithms as well as its application to replica-exchange methods such as parallel tempering. We briefly discuss a number of examples including low-temperature states of magnetic systems with competing interactions and dense liquids